Predict the crystal field energy-level diagram for a linear ML2 complex that has two ligands along the :

Video transcript

Welcome everybody. Our next question says for an ML subscript two complex, what is its crystal field energy level diagram? If it's two ligands are aligned along the plus or minus Z axis and it has a linear geometry, we have two diagrams, one with an xyz axis. However, it's oriented a little differently than usual in the plane of the screen, we have X pointing upward Z pointing to the right and then Y is pointing at an angle to indicate that it's pointing up out of the screen is the third dimension. So that's not often how these three dimensions are drawn. But for the sake of this problem, it's drawn this way because our molecule is linear and is aligned along the Z axis. So our molecule is shown as L for ligand bonded to M bonded to another L all in a straight line 180 degree bond angles. So to think about what the crystal field energy level diagram looks like, we would need to think about the d orbitals since they're what participates in that crystal field energy splitting, how they're oriented along these axes and therefore, which would have higher energy. So I will start by putting up just really quickly drawn diagrams of our different de orbital shapes and orientations so that we can think about which ones will be interacting more with the electrons in our molecule. So first to keep in mind is that four of them have these sort of clover leaf shape with four lobes. The three on the right DXY DXZ and DYZ are within the planes of the two axes in their name, but in between the axis themselves, so they don't point directly at the x axis or the Y axis, but are in between. Then we have the last clover shape, DX squared minus Y squared which is within the plane of X and Y. But sitting along those axes directly along those axes and pointing in those directions. Finally, we have our odd one out the DZ squared orbital which has sort of a doughnut in the center and then two lobes and this has a sort of linear alignment along the Z axis. So keeping in mind that the more directly the orbitals point at our electrons, the more repulsion there will be and therefore the more energetically unfavorable that orbital will be. So with that, in mind, we can see that the DZ squared orbital will have the highest energy it's aligned along that Z axis. And so since our whole linear molecules along that z axis, that will have the most repulsion between the electrons, they're going to overlap the most. So now let's think about the next level down, which would be two of those cloverleaf orbitals, DYZ and DXZ each are within the plane of the Z axis, but not pointing directly at our ligands. They're off at a 45 degree angle. So they'll be the next highest but lower than DZ squared since they don't point directly along the Z axis. So those two, which I've drawn along the bottom will be the second highest energy level. Then we have two orbitals left that are not in the Z plane at all DXY and DX squared minus Y squared. It doesn't matter from the point of view of our molecule, whether they're along the X and Y axis or off at an angle because they're not in that Z plane whatsoever. So those two will be the sa the same and they will be the lowest energy levels with our giant orbital diagrams taking up all the space here, I am going to have to scroll down to make room for the final energy level diagram. But again, for that linear molecule along the z axis, our energy level splitting will be two orbitals down at the lowest level, which will be the Xyz orbital and the X squared minus Y squared, those two that are not in the Z plane at all. And then our next level up will be the YZ and XZ. They are in the Z plane but not pointing directly along the z axis. So there's not as much repulsion as our highest level, which will be Z squared all by itself, since it does directly point at along with the axis and will directly point at those electrons of the ligands. So we have our crystal field energy level splitting two lower two in the middle and one the highest for this linear molecule. See you in the next video.